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Period Growth Rates & Compound Monthly Growth

Calculate month-over-month, quarter-over-quarter and year-over-year changes, plus compound monthly growth between two endpoint values.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

A value rising from 80 to 100 increases by 25%. Growth from 100 to 121 over two monthly intervals corresponds to a compound monthly rate of 10%.

Period change (%) = (new − old)/old × 100; CMGR = (last/first)^(1/months) − 1

Worked example

Enter these known values and leave the other values blank.

Value in month 1
80
Value in month 2
100
Value quarter 1
200
Value quarter 2
180
Value year 1
200
Value year 2
300
Value in first month
100
Value in last month
121
Elapsed monthly intervals
2 mos
Month-over-month change (%)
25 %
Compound monthly growth rate
10 %
Quarter-over-quarter change (%)
-10 %
Year-over-year change (%)
50 %

Assumptions and limitations

  • Starting values must be positive and ending values nonnegative. Percentage growth from a zero starting value is undefined in this model.
  • The compound duration is the number of elapsed monthly intervals, not the number of observations. January to March spans two intervals.
  • A zero ending value gives −100% compound growth for a positive duration. Intermediate volatility and cash flows are not described by the endpoint rate.
  • The three period comparisons and the compound calculation are independent. Use matching units and consistently defined metrics within each pair.

Common questions

Should I average the monthly percentages to get CMGR?

No. This calculation finds the constant compounded rate that connects the two endpoints over the stated number of intervals.

References

Bookify requires a positive starting value for compound monthly growth, avoiding a zero denominator while retaining a zero ending value.

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